"I really cut my teeth on off-off-off Broadway shows"

Bea Arthur's quote is a metaphor for acquiring experience in a particular field. By stating she "cut her teeth" on off-off-off Broadway programs, she is indicating that she got a great deal of experience in the theater market by carrying out in little, lesser-known productions. This experience was important in helping her become the effective actress she was. It is likely that she was referring to her early profession, when she was just starting out and had to take whatever roles she could get. By performing in these small productions, she was able to refine her craft and gain the experience she needed to ultimately become a successful starlet. Her quote is a testimony to the importance of getting experience in any field, no matter how little or irrelevant it may seem.